Question: Simplify the following expression: $k = \dfrac{40xz - 10z}{20z^2 + 10z} - \dfrac{30z^2 + 10z}{20z^2 + 10z}$ You can assume $x,y,z \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{40xz - 10z - (30z^2 + 10z)}{20z^2 + 10z}$ $k = \dfrac{40xz - 20z - 30z^2}{20z^2 + 10z}$ The numerator and denominator have a common factor of $10z$, so we can simplify $k = \dfrac{4x - 2 - 3z}{2z + 1}$